臺灣博碩士論文加值系統

本研究主要在於發展一套族群式最佳化演算法，應用於工程問題之最佳化求解。本演算法是以粒子群演算法為主要架構，並應用格點法以改進粒子群搜尋過程之效率。
為驗證本演算法，本文選擇11個標竿函數，含可分離函數與不可分離函數，且這些函數特性之極值包括單一極值及多極值等。為顯示本演算法對函數維度個數變化之執行效率，本文分別探討函數30維、50維及100維變數之求解。
由於函數求解之難易度與其是否為分離式或非分離式型態有密切關聯，本文引用灰色理論以判斷所求解問題變數間的交互強度。為作進一步突顯本方法之可行性，本文先以兩個工程實例進行運算求解驗證。
最後，本文將所發展之演算法用於滑蓋手機彈簧參數之最佳化設計。計算過程中是以ANSYS有限元素軟體進行應力數值計算分析，期望藉著本演算法以求解機件設計變數，以改善機件最大應力集中現象。

In this research, a numerical population-based optimization algorithm is developed for optimization problems, the algorithm is established based on the particle swarm optimization incorporated with the grid method.
To verify the proposed algorithm, we selected 11 benchmark functions, with variables interacted or non- interacted. Meantime, there are three different number of dimensions for each tested functions are considered, they are 30, 50 and 100 respectively. The results obtained by the proposed method are shown much improved than those from the particle swarm optimization.
Further, two engineering optimization design problems, a complicated gear problem and a plane-truss structure problem are solved by the proposed method. The results determined demonstrated the proposed method provide the solutions the same as the best ones obtained by other different approaches.
Finally, an optimization design of springs of a slider cell-phone is designed with 8 variables considered. The proposed method is applied on the mechanism to determine the combination of the eight variables to reduce the stress concentration as much as possible.
 

摘要 ii
Abstract iii
目錄 iv
圖目錄 vii
表目錄 xiii
第一章 緒論 1
1.1研究動機及目的 1
1.2 文獻回顧 2
1.3 研究方向與論文架構 9
第二章 改良式粒子群演算法 12
2.1 粒子群演算法 12
2.1.1 PSO速度更新模式 13
2.1.2 模擬PSO搜尋過程 17
2.2迭代式格點法 18
2.2.1格點法 18
2.2.2迭代式格點法流程步驟 21
2.2.3模擬迭代式格點法搜尋過程 22
2.3改良式粒子群演算法 24
第三章 標竿函數問題測試與結果討論 28
3.1標竿問題敘述 28
3.2 可分離與不可分離問題之檢視 39
3.2.1可分離與不可分離問題之圖形觀測 39
3.2.2可分離與不可分離問題之灰關聯度判定 45
3.3 改良式粒子群演算法與粒子群演算法性能測試與比較 56
3.4 小結 64
第四章 工程與結構最佳化之應用 67
4.1複式齒輪系最佳化問題 67
4.2 10桿桁架設計最佳化問題 71
4.3 小結 78
第五章 滑蓋手機彈簧最佳化設計 80
5.1滑蓋手機彈簧介紹 81
5.2結構力學基本理論 83
5.2.1 控制方程式 83
5.2.2 有限元素法 85
5.2.3有限元素法分析步驟 86
5.2.4 非線性分析 88
5.2.5 von Mises破壞準則 90
5.3接觸分析理論 91
5.3.1 接觸分析 91
5.3.2 接觸演算法 92
5.4模擬分析及實驗比對 94
5.4.1滑蓋彈簧之有限元素模型建立與分析 95
5.4.2模擬分析結果與實驗比對 98
5.5滑蓋手機彈簧可分離與不可分離問題判定 102
5.6滑蓋手機彈簧幾何形狀設計最佳化 104
5.6.1最佳化設計與分析流程 105
5.6.2滑蓋手機彈簧幾何最佳化設計(Ⅰ)之結果與討論 107
5.6.3滑蓋手機彈簧幾何最佳化設計(Ⅱ)之結果與討論 111
5.7結果討論 115
第六章 結論與未來展望 117
6.1結論 117
6.2未來展望 118
參考文獻 120

1. 劉惟信，“機械最佳化設計 ”，全華科技圖書股份有限公司，2001。
2. Acan, A. and A. Gunay,“Enhanced Particle Swarm Optimization through External Memory Support,”IEEE,pp.235-242(2005).
3. 羅俊彥，粒子群演算法於高維數全域最佳化問題，海洋大學造船工程研究所，碩士論文(2006)。
4. Dorigo, M., Maniezzo, V. and Coloni, A., “Positive Feedback as a Search Strategy.” Technical Report, No.91-016, Politecnico di Milano, Itaaly (1991).
5. Reynolds, R.G. and Sverdlik, W., “Problem Solving using Cultural Algorithms.” Evolutionary Computation, IEEE World Congress on Computational Intelligence, Proceedings of the First IEEE Conference on Vol.2, pp.645-650 (1994).
6. Kennedy, J. and Eberhart, R.C., “Particle Swarm Optimization.” Proc. IEEE International Conf. Neural Networks, Vol.4, pp. 1942-1948(1995).
7. Shi, Y. and Eberhart, R.C., “A Modified Particle Swarm Optimizer.” IEEE Int. Conf. on Evolutionary Programming, pp. 69-73(1998).
8. Angeline, P.J., “Using Selection to Improve Particle Swarm Optimization.” IEEE World Congress on Computational Intelligence, pp. 84-89(1998).
9. Shi, Y. and R.Eberhart, “Empirical Study of Particle Swarm Optimization.” Proceeddings of the 1999 Congress on Evolutionary Computation, Washington, DC, IEEE, Piscataway, NJ,USA, Vol. 3, pp.1945-1950,(1999).
10. Suganthan, P.N., “Particle Swarm Optimiser with Neighbourhood Operator.” Proceeddings of the 1999 Congress on Evolutionary Computation, Washington, DC, IEEE, Piscataway, NJ,USA, Vol. 3, pp.1958-1962,(1999).
11. James Kennedy , “Small Worlds and Mega-Minds:Effects of Neighborhood Topology on Particle Swarm Optimization Performance.” Proceeddings of the 1999 Congress on Evolutionary Computation, Washington, DC, IEEE, Piscataway, NJ,USA, Vol. 3, pp.1931-1938,(1999).
12. Clerc, M. and J. Kennedy, “The Particle Swarm:Explosion, Stabiliry, and Convergence in a Multimodal Complex Space.” Proceeddings of the Congress of Evolutionary Computation, Washington, DC, IEEE, Piscataway, NJ,USA, Vol. 6, pp.58-73,(2000).
13. Eberhart, R.C. and Shi, Y. “Tracking and Optimizing Dynamic Systems with Particle Swarms.” Proceedings of the Congress on Evolutionary Computation, Vol 1, 94–100, Soul, IEEE Press(2001).
14. Fourie, P.C. and A.A. Groenwold, “The Particle Swarm Optimization Algorithm in Size and Shape Optimization.” Structural and Multidisciplinary Optimization, Springer Verlag, Vol 23, pp.259–267, (2002).
15. Chatterjee, A. and P. Siarry, “Nonlinear Inertia Weight Variation for Dynamic Adaptation in Particle Swarm Optimization.” Computers and Operations Research, Vol. 33,pp.859-871(2004).
16. Zhang, Li-Ping, Huan-Jun. Yu, and Shang-Xu. Hu. “Optimal Choice of Parameters for Particle Swarm Optimization.” Journal of Zhejiang University:Science, Vol. 6,pp.528-534,China(2005).
17. Liu Bo, Ling Wang, Yi-Hui Jin, Fang Tang and De-Xian Huang, “Improved Particle Swarm Optimization Combined with Chaos.” SCI Chaos, Solitons and Fractals, Vol.25,pp.1261-1271(2005).
18. 劉清祥，粒子群演算法於結構設計及零工式排程之應用，海洋大學造船工程研究所，碩士論文(2005)。
19. S. Fan, Shu-Kai and Erwie Zahara, “A Hybrid Simplex Search and Particle Swarm Optimization for Unconstrained Optimization.” European Journal of Operational Research, Vol. 181, pp.527-548(2006).
20. Guangyou Yang, Dingfang Chen and Guozhu Zhou,“A New Hybrid Algorithm of Particle Swarm Optimization.” Lecture Notes in Computer Science, Volume 4115/2006, 50-60 (2006).
21. 蘇昱豪，具隨機粒子與微調機制式粒子群最佳化於多極值問題之研究，台灣科技大學機械工程系研究所，碩士論文(2006)。
22. 陳韋帆，空間鑑定演算法活化PSO之全域最佳化設計，海洋大學造船工程研究所，碩士論文(2007)。
23. 陳慶忠，鷹群掠食演算法於全域最佳化設計之研究，海洋大學造船工程研究所，碩士論文(2008)。
24. Li Xiang, Liang Ximing, M. Fikret Ercan and Zhou Yi ,“A New Hybrid Algorithm Based on Collaborative Line Search and Particle Swarm Optimization.” Proceedings of the 4th International Conference on Autonomous Robots and Agents, Feb 10-12(2009).
25. Yin, P.Y., Glover, F., Laguna M., and Zhu J-X., “Cyber Swarm Algorithms–Improving Particle Swarm Optimization Using Adaptive Memory Strategies”, European Journal of Operational Research 201 (2), 377-389(2010).
26. Huoming Zhang, Mingzheng Gao and Xiaofei Zhang, “Improved Hybrid Particle Swarm Optimization Algorithm.” 2010 Sixth International Conference on Natural Computation(ICNC 2010).
27. 蒲志昌，智慧型鷹群掠食演算法於全域最佳化問題及輪胎花紋節距排列之應用，海洋大學造船工程研究所，碩士論文(2010)。
28. Mohammed EI-Abd, “A Hybrid ABC-SPSO Algorithm for Continuous Function Optimization.” Swarm Intelligence (SIS), 2011 IEEE Symposium on 978-1-61284-053-6, IEEE Press(2011).
29. 林明璋，滑蓋手機之機構研究，逢甲大學材料與製造工程所，碩士論文(2007)。
30. 陳盈璋，滑蓋彈簧應力分析與尺寸參數設計，國立台灣科技大學機械工程系，碩士論文(2007)。
31. 馬揚傑，扭力彈簧之電腦輔助應力分析，國立台灣科技大學機械工程系，碩士論文(2008)。
32. 蔡意輝，滑蓋彈簧之壽命分析，國立台灣科技大學機械工程系，碩士論文(2008)。
33. 張敬民，應用基因演算法於滑蓋手機彈簧結構最佳化設計，國立高雄第一科技大學機械與自動化工程所，碩士論文(2009)。
34. 胡曉輝，「粒子群優化算法介紹」，<http://web.ics.purdue.edu/ ~hux/tutorials.shtml> (2002)。
35. Kennedy, J., Eberhart, R.C. and Shi, Y., “Swarm Intelligence.” Morgan Kaufmann division of Academin Press (2001).
36. Eberhart, R.C. and Shi, Y., “Comparison between Genetic Algorithms and Particle Swarm Optimization.” Lecture Notes in Computer Science; Vol.1447, pp611-616(1998).
37. Ke Tang , Xiaodong Li , P. N. Suganthan , Zhenyu Yang , and Thomas Weise , “Benchmark Functions for the CEC’2010 Special Session andCompetition on Large-Scale Global Optimization.” Nanyang Technological University (NTU), Singapore, Tech. Rep. January.8.2010.[Online].Available:http://sci2s.ugr.es/EAMHCO/cec2010_functions. Pdf
38. 巫衍毅，改良式差分進化演算法應用於輪胎花紋噪音及動態系統之振動控制，海洋大學造船工程研究所，碩士論文(2010)。
39. 陳奕丞，基於直交表之迭代式搜尋法於實驗設計問題，海洋大學造船工程研究所，碩士論文(2007)。
40. H. Schmidt, and G. Thierauf, “A combined heuristic optimization technique.” Advances in Engineering Software 36, pp.11–19,(2005).
41. 謝阜錝，結構最佳化設計之新式協力進化遺傳演算法，國立台灣大學機械工程學系研究所，碩士論文(2002)。
42. Deb K., and Goyak M., “A Combined Genetic Adaptive Search (GeneAS) for Engineering Design.” Computer Science and Informatics, vol.26, No.4, pp.30-45,(1996).
43. Wu Shyue-Jian, and Chow Pei-Tse, “The Applications of Genetic Algorithms to Discrete Optimization Problems.” Journal of the Chinese Society of Mechanical Engineers, vol.16, No.6, pp.587-598.(1996).
44. Rajeev S, and Krishnamoorthy CS, “Discrete optimization of structures using genetic algorithm. ” J Struct Eng, 118:pp.1233–50, (1992).
45. Galante M, “Genetic algorithms as an approach to optimize real-world trusses. ” Int J Numer Methods Eng, 39:pp.361–82,(1996)
46. 李輝煌，“ANSYS工程分析基礎與觀念”，高立圖書有限公司，2009。
47. ANSYS , Inc. Release 11.0 Documentation for ANSY,2007.
48. 劉晉奇、褚晴暉，“有限元素分析與ANSYS的工程應用”， 滄海書局， 2006。